Speaking at his home in Argentina, Horacio Sala said he was "desperate" after a privately-funded search operation found the aircraft in waters north of Guernsey on Sunday.

"I cannot believe it. This is a dream. A bad dream. I am desperate," Sala told local broadcaster Cronica TV.

The Piper Malibu carrying 28-year-old Sala and pilot David Ibbotson, 59, disappeared over the English Channel after leaving Nantes in France for Cardiff.

Two vessels, including one commissioned by the AAIB, had been taking part in a fresh search covering an area of around four square nautical miles on Sunday when the wreckage was located.

Emiliano Sala booklet. Image: Getty Images.

Marine scientist David Mearns, the director of Blue Water Recoveries, led a team on the search vessel FPV Morven while the AAIB also sent a team aboard the Geo Ocean III, a specialist vessel commissioned for the task.

The privately-funded operation on behalf of the Sala family was made possible after a campaign raised more than STG260,000 ($A470,175) to pay for it.

The plane had requested to descend before it lost contact with Jersey air traffic control.

An official search operation was called off on January 24 after Guernsey's harbour master Captain David Barker said the chances of survival following such a long period were "extremely remote".

Two seat cushions, which are likely to have come from the plane, were found last week on the French coast.

Cardiff had signed the footballer for a club record STG15 million and he was due to start training last month.